Problem: Rewrite as a simplified fraction. ${0.\overline{3} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 3.3333...\\ 1x &= 0.3333...\end{align*}}$ Subtracting the two equations, we have: ${9x = 3}$ ${x = \dfrac{3}{9}} $ ${x = \dfrac{1}{3}} $